The win boosts North Dakota's chances of earning one of the top three seeds in the Big Sky Conference tournament if it can beat Southern Utah Thursday.
Jaron Nash added 14 points and North Dakota (15-14, 12-7 Big Sky) was outshot 60.4 percent to 58 percent, but made 32 of 42 free throws to 22 of 28 for the Bears (16-12, 10-9).
North Dakota pulled ahead 27-26 on a jumper by Nash and led 56-43 at halftime.
Northern Colorado used a 10-2 second-half run to close to 69-63, then pulled to within four after Jordan Wilson scored six straight points.
Darrick Barden led the Bears with 17, Tevin Svihovec 16, Tate Unruh 13 and Tim Huskisson 10.